Wallace, 37, was from Dallas and had moved to Oklahoma last year. He lived for a time in an Oklahoma City homeless shelter. He had an arrest record in Texas for violent crimes.
Wallace did not know the girl, who was with her mother at the store, police reported earlier. He picked her out of a shopping cart.
The district attorney told The Oklahoman on Friday that Midwest City police officers saved the child's life. He said Wallace obviously was mentally ill.
Police reported finding a notebook and three-ring binder with religious writings in Wallace's Midwest City apartment after the shooting. Police reported Wallace spoke, while holding the girl hostage, about “Illuminati.”
A Midwest City police detective described the “Illuminati” as a satanic cult. Historically, it was the name of a secret society in the 1700s. It also is the name given to a group in a novel by popular author Dan Brown.
The police chief, Clabes, said Friday he expects Huff will return to duty next week.